It looks as though Fraunhofer has been working on this for a while. There are at least three big, interesting problems that need to be solved in order to roll out a system like this.

First, a database of melodies needs to be created, and preferably in an automated way, which would require the dynamic identification and transcription of a vocal or instrumental melody from among the other musical parts of a recording. Second, a user's hummed query needs to be analyzed to identify relative pitches and rhythm. Finally, the user's query must be run against the database. Due to variations in humming ability and the accuracy of remembered melodies, the search engine needs to effectively find near or partial matches.

When all of these problems have been effectively dealt with there will be a many uses aside from the search engine. Automated transcription alone would be of great value to individual musicians, composers, and arrangers, not to mention sheet music publishers. Where can I get my hands on this stuff?